https://hal.inria.fr/hal-01648135Avrachenkov, KonstantinKonstantinAvrachenkovNEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - MÃ©diterranÃ©e - Inria - Institut National de Recherche en Informatique et en AutomatiqueChebotarev, PavelPavelChebotarevICS RAS - Trapeznikov Institute of Control Sciences - RAS - Russian Academy of Sciences [Moscow]Mishenin, AlexeyAlexeyMisheninSPBU - Saint Petersburg UniversitySemi-supervised Learning with Regularized LaplacianHAL CCSD2017Semi-supervised learningGraph-based learningRegularized LaplacianProximity measureWikipedia article classification[INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Avrachenkov, Konstantin2017-11-24 18:30:302023-03-15 08:58:092017-11-27 11:40:04enJournal articleshttps://hal.inria.fr/hal-01648135/document10.1080/10556788.2016.1193176application/pdf1We study a semi-supervised learning method based on the similarity graph and Regularized Laplacian. We give convenient optimization formulation of the Regularized Laplacian method and establish its various properties. In particular, we show that the kernel of the method can be interpreted in terms of discrete and continuous time random walks and possesses several important properties of proximity measures. Both optimization and linear algebra methods can be used for efficient computation of the classification functions. We demonstrate on numerical examples that the Regularized Laplacian method is robust with respect to the choice of the regularization parameter and outperforms the Laplacian-based heat kernel methods.